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United States Patent |
5,170,671
|
Miau
,   et al.
|
December 15, 1992
|
Disk-type vortex flowmeter and method for measuring flow rate using
disk-type vortex shedder
Abstract
An axisymmetric bluff body is proposed for a vortex flowmeter as the vortex
shedder. It is found that vortex shedding frequencies measured can be
nondimensionalized into a linear relation with the Reynolds number for
area blockage ratios of circular disks up to 29.2%. Vortex shedding
frequency can be clearly sensed by a pressure transducer installed on the
pipe wall in the neighborhood of the maximum pressure fluctuation being
measured. This suggests a feasible design that the sensor of a vortex
flowmeter can be removed from the flow field or changed easily.
Inventors:
|
Miau; Jiun-Jih (Tainan, TW);
Liu; Tzu-Wen (Taichung, TW);
Chou; Jung-Hua (Shinchu, TW);
Chen; Tzu-Liang (Tainan, TW)
|
Assignee:
|
National Science Council (TW)
|
Appl. No.:
|
758676 |
Filed:
|
September 12, 1991 |
Current U.S. Class: |
73/861.22 |
Intern'l Class: |
G01F 001/32 |
Field of Search: |
73/861.52,861.22,861.24,861.21
|
References Cited
U.S. Patent Documents
4638672 | Jan., 1987 | McCall | 73/861.
|
Foreign Patent Documents |
2928568 | Jan., 1981 | DE | 73/861.
|
Primary Examiner: Goldstein; Herbert
Attorney, Agent or Firm: Marks & Murase
Claims
What is claimed is:
1. A vortex shedder disposed in a conduit facing an incoming flow,
comprising:
an axisymmetric bluff body comprising a circular disk facing said incoming
flow, said disk having a sharp edge bevelled at an angle less than
90.degree., wherein said bluff body has a blockage ratio less than 29.2%;
and
support means for supporting said disk in said conduit such that a wake
produced by said support means is negligible in comparison to a wake
produced by said disk.
2. A method for detecting a mean velocity of an incoming flow in a conduit,
comprising:
preparing an axisymmetric bluff body having a circular disk facing incoming
flow, said disk having a sharp edge bevelled at an angle less than
90.degree. and said disk having a blockage ratio less than 29.2%;
supporting said bluff body in a conduit such that a substantial wake is
produced by said disk;
obtaining a vortex shedding frequency of said substantial wake; and
obtaining the mean velocity from a relationship between said vortex
shedding frequency and the mean velocity of the incoming flow.
3. The method for detecting a mean velocity of an incoming flow in a
conduit as claimed in claim 2, further comprising:
recording a fluctuating wall pressure signal of said substantial wake,
wherein
said vortex shedding frequency is obtained from said wall fluctuating wall
pressure signal.
4. The method for detecting a mean velocity of an incoming flow in a
conduit as claimed in claim 3, wherein:
said step of obtaining said vortex shedding frequency is performed by
spectral analysis.
5. The method for detecting a mean velocity of an incoming flow in a
conduit as claimed in claim 3, wherein
said step of obtaining said vortex shedding frequency is performed by
filtering.
6. The method for detecting a mean velocity of an incoming flow in a
conduit as claimed in claim 3, wherein:
said wall pressure fluctuating signal is recorded at a position downstream
from said bluff body by a distance about 2.5 times as long as the diameter
of said disk.
Description
BACKGROUND OF THE INVENTION
1. Technical Field of the Invention
The present invention relates to a flowmeter for detecting flow rate in a
pipe or a tube. The present invention relates more particularly to a
vortex flowmeter.
2. Description of Related Art
Since flow rate is an primary variable in fluid dynamics, how to measure
flow rate in a pipe or a tunnel, which is called an inner flow, becomes
important in scientific researches and industrial applications.
Plural methods can be used to measure the flow rate in different
conditions. As a most simple example, in a fully developed laminar pipe
flow, we can easily get the measurement of flow rate after we had
determined the velocity at a point and the location of this point and the
diameter of the pipe. Besides, several commercially available flowmeters
are briefly discussed below.
Orifice meters have been by far the most popular for years. The principle
behind orifice meters is that, a differential pressure transmitter
measures pressure drop across a restriction in the line. The restriction
is usually a concentric orifice, with the orifice diameter being 10% to
75% of the inside pipe diameter. The pressure drop can be measured with
flange taps. The simplified equation,
F=C P
where F=volumetric flow rate, P=differential-pressure measurement, and C
orifice coefficient, represents the relations between flow rate and
pressure difference.
The orifice meter provides a time-proven and relatively low-cost approach
for measuring most flows. But, the orifice meter does have its
limitations, in that under certain situations, for various reasons, it
will not work. For liquid service, these cases include systems where: the
necessary pressure drop in not available (in most gravity-flow
applications); the fluid will flash at the reduced pressure that occurs in
the throat of the orifice meter; or flow rate is high.
About the orifice meter, since flow is related to the square root of the
pressure drop, it requires a square-root extractor between the output of
the differential pressure transmitter and a flow controller in order to
give a linear relationship, which is at the sacrifice of cost and
accuracy.
Other differential pressure type meters include: venturi meter, flow
nozzle, annular orifice gentile tube, wedge meter, integral orifice, pitot
tube, elbow meter, variable area meter, target meter, sonic nozzle,
multi-port pitot, dall tube, variable aperture meter, etc.
Positive displacement meters operated by using mechanical divisions to
successively displace discrete volumes of fluid. This principle of
operation is essentially simple, but the accuracy depends upon precision
in both manufacture and assembly.
A common used positive displacement meter is the rotary piston meter. This
employs a cylindrical piston which is displaced around a cylindrical
chamber by the flowing liquid. Rotation of the piston drives an output
shaft which is used to operate counters. Rotary piston meters can handle a
wide range of process liquids with a large range of viscosity.
Other positive displacement type meters include: reciprocating piston,
sliding vane, nutating disc, oval gear, helix meter, bi- and tri-rotors,
metering pump, roots blower, diaphragm meter, wet gas meter, bellows
meter, etc.
The principle of operation of inferential type meters uses a rotating
component (wheel, vane, rotor or helical runner) to convert free stream
energy into rotary motion. This rotary motion is then detected by some
type of pick-up device, i.e. magnetic, optical, radio frequency, or gears
and a mechanical counter. Axial turbines are the most widely available and
accurate type of inferential type meters.
Vortex shedding meter is the most commonly used among fluid oscillatory
type meters. A vortex flowmeter detects frequency of vortex shedding from
a bluff body which, as learned from fluid dynamics, is linearly
proportional to the fluid velocity under certain conditions. Relevant
papers discussing this phenomenon can be found in: H. V. Mangin, Tappi 58,
65 (1975); D. J. Lomax, Control Instrument 7, 36 (1975); and T. J. S.
Brain and R. W. W Scott, J. Phys. E 15, 967 (1982).
Conventional vortex flowmeter is a two dimensional bluff body accommodating
a pressure sensor or a probe for detecting vortex shedding frequencies.
The bluff body is across the flow field with its front face facing the
stream as shown in FIG. 1A and 1B. The upper edge and lower edge of the
front face form sharp angles with the front face. As fluid flows under
certain conditions, vortices alternatively develop behind both edges of
the bluff body. The shedding frequency is defined as the number of
vortices developed in a certain time. Since shedding frequency is linearly
proportional to the flow speed, flow speed can be easily evaluated. The
accuracy of vortex flowmeter is relatively high in a wide range of flow
speed. The turndown ratio, which is the maximum measurable flow rate over
the minimum measurable flow rate, is up to 100 to 1, at an accuracy of
0.5% of meter reading.
The vortex flowmeter has been well accepted as a competitor for accurate
and inexpensive flow rate measurement. Current vortex flowmeters are
designed with a two-dimensional-like bluff body together with a sensor
that is either integrated into the bluff body or separately situated
downstream for detecting the vortex shedding frequency, as described in M.
Takamoto and K. Komiya, J. Fluid Control 11, 27 (1979), and P. G. Scott,
"Use of Vortex Flowmeters for Gas Measurements," J. Petroleum Technol. 33,
2082 (1981).
It is considered that the maintenance and replacement of pressure sensor is
not quite easy. Pressure sensor could not be detached from the bluff body
unless the pipe is disconnected. This is due to the limitation of the
design of two dimensional bluff body because pressure sensor must be
placed behind the bluff body. In an experiment, one can not know whether
the probe works precisely or not. Even he (she) knows the error arises
from the probe, changing the probe may change the structure of flow field.
Other types of flowmeters not described above includes: electromagnetic
meters, ultrasonic meters, mass meters, thermal meters, miscellaneous
meters, solids meters, open channel meters, etc.
SUMMARY OF THE INVENTION
It is therefore an object of this invention to provide a vortex flowmeter
that is easy to service the probe or sensor.
This object of the present invention are fulfilled by providing an
axisymmetric bluff body with a sharp edge for the vortex flowmeter, and a
pressure sensor installed on the pipe wall. The pressure fluctuations of
vortices, at the same frequency of vortex shedding frequency, can be
sensed by the pressure sensor.
The present study considers a practical application that an axisymmetric
bluff body could be placed in a circular pipe as a vortex shedder, then
the resultant wake affects flow near the wall to behave unsteadily. This
unsteady characteristic is then picked up by a pressure sensor installed
on the wall. And then, the vortex shedding frequencies of the wake were
correlated with the Reynolds numbers of the flow. The present invention
further provides a nondimensionalization scheme that considered the
blockage effect of the circular disk and would correlate the reduced
frequencies with the Reynolds numbers linearly, for area blockage ratios
up to 29.2%. The area blockage ratio BR was defined as d.sup.2 /D.sup.2,
where d and D were the diameters of the circular disk and the circular
pipe, respectively. Detecting vortex shedding frequency from wall pressure
fluctuations was feasible if the measured location was chosen properly.
Further scope of applicability of the present invention will become
apparent from the detailed description given hereinafter. However, it
should be understood that the detailed description and specific examples,
while indicating preferred embodiments of the invention, are given by way
of illustration only, since various changes and modifications within the
spirit and scope of the invention will become apparent to those skilled in
the art from this detailed description.
BRIEF DESCRIPTION OF THE DRAWINGS
The present invention will become more fully understood from the detailed
description given hereinbelow and the accompanying drawings which are
given by way of illustration only, and thus are not limitative of the
present invention and wherein:
FIG. 1A is a front view of a conventional two dimensional bluff body
installed in a pipe;
FIG. 1B is a cross-sectional side view of a conventional two dimensional
bluff body installed in a pipe;
FIG. 2A is a front view of a disk-type bluff body according to the present
invention installed in a pipe;
FIG. 2B is a cross-sectional side view of a disk-type bluff body according
to the present invention installed in a pipe, including a pressure sensor,
spectral analyzer and filter.
FIG. 3A shows the distributions of St* vs Re.sub.d * in a range of 2.5
.times. 10.sup.3 -9.7 .times. 10.sup.4 ;
FIG. 3B shows the distributions of St vs Re.sub.d in a range of 2.5 .times.
10.sup.3 -9.7 .times. 10.sup.4 ;
FIG. 4A shows the mean pressure distribution in terms of
P.infin.-P/1/2.rho.U.sup.2 .smallcircle., for disk A;
FIG. 4B shows the root-mean-square pressure fluctuation distributions, for
disk A;
FIG. 4C shows the mean pressure distribution in terms of
P.infin.-P/1/2.mu.U.sup.2 .smallcircle., for disk B;
FIG. 4D shows the root-mean-square pressure fluctuation distributions
P'.sup.2.sup.1/2 /1/2.rho.U.sup.2 .smallcircle., for disk B:
FIG. 5A shows the raw pressure signal obtained for disk B at X/d=2.14,
Re.sub.d.sup.* ==3.7.times.10.sup.4 ;
FIG. 5B shows the high-pass variations of the signal trace shown in FIG.
5A;
FIG. 6A shows the raw pressure signal obtained for disk A, Re.sub.d.sup.*
=1.1.times.10.sup.4, at X/d=-0.15;
FIG. 6B shows the frequency spectra of wall pressure fluctuation obtained
for disk A, Re.sub.d.sup.* =1.1.times.10.sup.4, at X/d=-0.15;
FIG. 6C shows the raw pressure signal obtained for disk A, Re.sub.d.sup.*=
1.1.times.10.sup.4, at X/d=1.2;
FIG. 6D shows the frequency spectra of wall pressure fluctuation obtained
for disk A, Re.sub.d.sup.* =1.1.times.10.sup.4, at X/d=1.2;
FIG. 6E shows the raw pressure signal obtained for disk A, Re.sub.d.sup.*
=1.1.times.10.sup.4, at X/d=2.5;
FIG. 6F shows the frequency spectra of wall pressure fluctuation obtained
for disk A, Re.sub.d.sup.* =1.1.times.10.sup.4, at X/d=2.5;
FIG. 6G shows the raw pressure signal obtained for disk A, Re.sub.d.sup.*=
1.1.times.10.sup.4, at X/d=3.3; and
FIG. 6H shows the frequency spectra of wall pressure fluctuation obtained
for disk A, Re.sub.d.sup.* =1.1.times.10.sup.4, at X/d=3.3.
DETAILED DESCRIPTION OF THE EMBODIMENTS
The present invention utilizes a circular disk to be a vortex shedder. The
circular disk 1, as shown in FIG. 2A and 2B, has a sharp edge 2 which is
bevelled. Circular disk 1 is fixed at the center of tunnel 3 by wires 4,
with its larger side facing the fluid flow. The effects of this kind of
vortex shedder are discussed below in some experiments, which is an
excerpt from the inventor's paper, "Vortex flowmeter designed with wall
pressure measurement", J. J. Miau, and T. W. Liu, Rev. Sci. Instrum. Vol.
61, p.2676 (1990).
EXPERIMENTS ON THE PRESENT INVENTION
Experiments were carried out in a low-speed closed-return water tunnel. The
test section is circular in cross section, D=148 mm, and is 800 mm long.
The velocity in the test section can be controlled in a range of 1-60
cm/s. At the inlet of test section, the turbulence intensity normalized by
the mean velocity measured at the core of the inlet, U.sub.o is about
0.9%.
A Venturi flowmeter providing a reference of flow rate is installed
downstream of the pump. The bulk velocity deduced from the flowmeter is
found to be very close to U.sub.o. This signifies that flow enters the
test section is uniform with a thin boundary layer. A survey of the mean
velocity profile at the inlet of the test section using a laser
velocimeter indicates that the boundary-layer thickness is less than 7 mm,
while the velocity distribution outside the boundary layer is uniform.
In this study, vortex-shedding phenomenon necessary for flow rate
measurement was produced by a circular disk situated in the test section,
see FIGS. 2A and 2B. This circular disk was held normal to the flow
direction by six stainless-steel wires of 0.2 mm in diameter. Under the
maximum operating U.sub.o condition, the Reynolds number based on the
diameter of the wires was about 130. Wakes resulting behind the wires were
found to be negligible in comparison with the wake behind the circular
disk. As seen in FIGS. 2A and 2B, the circular disk has the sharp edge
facing the incoming flow which is bevelled at an angle less than 90o This
ensures that flow is separated from the circular disk at the edge
irrespective of Reynolds numbers. Six sizes of circular disks were
employed in this study. Their diameters, denoted as d, are 30, 52, 70, 75,
80, and 88 mm, corresponding to area blockage ratios of 4.1%, 12 3%,
22.3%, 25.6%, 29.2%, and 35.4%, respectively.
A laser velocimeter of two-color and three-beam system, DANTEC LAD10, was
employed for obtaining vortex shedding frequency in the wake behind the
circular disk. The results provide a reference for wall pressure data to
compare with.
Wall pressure distributions in the streamwise direction were obtained with
a differential-type pressure transducer, Validyne DP-103. Originally this
pressure transducer served for time-mean pressure measurement, because its
frequency response is limited below 50 Hz. However, as found in the
present flow, frequencies associated with wall pressure fluctuations were
normally lower than 10 Hz. Thus this pressure transducer was capable of
measuring pressure fluctuations as well.
Laser-Doppler velocity measurements performed in the wake behind the
circular disk indicate that regular vortex shedding phenomenon can be
found in the cases with circular disks of area blockage ratios below
29.2%. Further, these frequencies measured, denoted as f, can be
normalized by d and U.sub.max into a unified relation, where U.sub.max is
the mean streamwise velocity of the flow outside the maximum width of the
separation bubble. In the experiment, U.sub.max was obtained from the
Bernoulli's equation with the time-mean wall pressure at the streamwise
location corresponding to the maximum width of the separation bubble
behind the circular disk, U.sub.o, and the wall pressure at a reference
location 26 cm upstream of the circular disk being known (relative
discussions can be found in A. M. K. P. Taylor and J. H. Whitelaw, J.
Fluid. Mech. 139, 391 in 1984). The data of St.sup.* (=fd/U.sub.max) of
different circular disks are plotted against Reynolds numbers in FIG. 3A,
where Re.sub.d.sup.* =U.sub.max d/.gamma. and .gamma. is the kinematic
viscosity of water. It is seen that these data points appear to collapse
into a single curve. A linear regression of these data points further
indicate that this curve can be described by
St.sup.* =K.sub.1 +K.sub.2 Re.sub.d.sup.* (1)
K.sub.1 and K.sub.2 are the nondimensional coefficients, where K.sub.1
=0.130, K.sub.2 =5.20.times.10.sup.-7. As seen in FIG. 3A, correlations
between the data points and the linear curve are quite good, characterized
by a correlation coefficient of 0.897. For comparison, FIG. 3B shows the
distributions of St versus Re, as the conventional definitions of
St=fd/U.sub.o and Re.sub.d = U.sub.o d/.gamma. for flow without blockage
effect. Apparently, the data points of different blockage ratios scatter
in a manner that the values of St increase with the blockage ratios, and
it is not meaningful to correlate all the data points with a linear curve.
As noted St.sup.* retrieves to St when U.sub.max =U.sub.o, i.e., the
blockage effect is negligible.
U.sub.max signifies the aerodynamics blockage effect due to the presence of
the circular disk in the circular pipe. Following Lefebvre (A. H.
Lefebvre, CoA Report Aero. No. 188 in 1965), U.sub.max can also be
obtained from the following expression, as a function of U.sub.o and BR:
##EQU1##
A comparison of the values of U.sub.max /U.sub.o obtained from (2) and the
values of U.sub.max /U.sub.o obtained from experiments is given in Table
I, which indicates that the discrepancies for all the cases studied are
less than 8%. Since the discrepancies appear in a manner that the
numerical values resulted from (2) are systematically lower than the
experimental data, the expression of (2) could be further modified in
improving the prediction of U.sub.max /U.sub.o.
TABLE I
______________________________________
Values of U.sub.max /U.sub.o obtained from experiment and from Eq. (2).
BR 4.1% 12.3% 22.3% 25.6% 29.2% 35.4%
______________________________________
(U.sub.max /U.sub.o).sup.a
1.11 1.36 1.76 1.88 2.03 2.30
(U.sub.max /U.sub.o).sup.b
1.09 1.31 1.62 1.74 1.89 2.16
______________________________________
.sup.a Experimental values.
.sup.b Values calculated from Eq. (2).
At present, one may combine the expressions of (1) and (2) into the
following form:
##EQU2##
Therefore,
AU.sup.2.sub.0 +BU.sub.0 +C=0, (5)
where A=K.sub.2 dj.sup.2 /.gamma., B=K.sub.1 J, and C=fd. Hence,
##EQU3##
Thus, U.sub.o can be obtained from (6) if f, d, BR, .gamma., K.sub.1, and
K.sub.2 are known. Hand calculations with (2) for a case with the circular
disk of BR=25.6% and f=1.9 Hz obtained from laser velocimeter measurement
give U.sub.o to be 48.4 cm/s. This value is about 7% higher than U.sub.o
=45.2 cm/s measured in the flow. This discrepancy is noticed mainly due to
the fact that the expression of (2) does not predict the ratio of (U.sub.o
/U.sub.max) accurately enough. For practical use, a calibration procedure
to modify the expression of (2) is necessary.
From a practical standpoint, there is no point to design a vortex flowmeter
with circular disk whose size is too large to result in unnecessary
momentum loss. On the other hand, the circular disk has to be large enough
in order that the unsteady characteristic of the wake is reflected from
flow development near the wall. On the basis of these considerations, two
cases of the circular disks whose area blockage ratios are 12.3% and
22.3%, denoted as disks A and B, respectively, are studied further.
Wall pressure distributions along the streamwise direction obtained for
these two cases are shown in FIG. 4A-4D. In this figure, the quantities of
mean pressure, in terms of P.infin.-P, and root-mean-square pressure
fluctuation, P'.sup.2.sup.1/2, are normalized by the dynamic pressure,
1/2.rho.U.sub.o.sup.2, where P.infin. is the reference wall pressure
measured at 26 cm upstream of the circular disk, .rho. is the density of
water, and d denotes the streamwise coordinate with X=0 at the frontal
face of the circular disk. In this figure it is noted that in each of the
cases the maximum root-mean-square pressure fluctuation occurs downstream
of the location where the minimum mean pressure or the maximum value of
P.infin.-P is measured. An earlier work (T. W. Liu, Masters thesis,
Institute of Aeronautics and Astronautics, National Cheng-Kung University
in 1989) indicates that the location of the minimum wall pressure measured
coincides with the location of the maximum width of the separation bubble,
while the location of the maximum root-mean-square pressure fluctuation
measured signifies the occurrence where the influence of the wake eddies
on the boundary layer developed on the wall is the most pronounced.
The unsteady behavior of the wall pressure signal is shown in FIG. 5A by a
segment of raw pressure signal obtained for disk B at X/d 2.14, downstream
of the location where the maximum root-mean-square pressure fluctuation is
measured. As seen, the signal trace mainly consists of variations of a
low-frequency component whose time scale is of the order 6-7 s and a
high-frequency component whose time scale is of the order 1 s.
Laser-Doppler velocity measurements confirm that vortex shedding frequency
of the wake coincides with the characteristic frequency associated with
the variations of the higher-frequency component in the signal. Thus,
variations of the lower-frequency component are suggested due to the
deformation of the separation bubble. If one performs a spectral analysis
of the signal one would find that energy resided in the component of
vortex shedding frequency is relatively small, compared to that in the
lower-frequency component. This presents a difficulty in identifying the
vortex shedding frequency. However, if an appropriate high-pass filtering
process is employed to the signal trace before performing spectral
analysis, the situation is expected to improve greatly, see FIG. 5B for
example.
To minimize the usage of the filtering technique, one alternately searches
for a location where the pressure fluctuations measured are dominated by
the vortex shedding frequency component. FIGS. 6A-6H compares the
frequency spectra obtained for disk A at X/d=-0.15, 1.2, 2.5, and 3.3,
when Re.sub.d.sup.* =1.1.times.10.sup.4. The raw signals associated with
these spectra are also included in the figure for reference. It is known
in advance from LDV measurements that the vortex shedding frequency under
this flow condition is 0.55 Hz. Among the four spectra shown in this
figure, the one obtained at X/d=1.2 shows the least favorable situation
that the components of lower frequencies dominate. Coincidentally, X/d=1.2
is about the location where the minimum mean pressure is measured, see
FIG. 4. The frequency spectrum obtained at X/d 2.5 shows the most
favorable situation that the vortex shedding frequency component appears
to be a predominant peak. Moreover, the energy resided in this frequency
component is about an order of magnitude higher than that of the same
frequency component seen in the spectrum obtained at X/d=3.3. The position
X/d is noted to be slightly downstream of the location where the maximum
wall pressure fluctuation is measured. It is also interesting to point out
that at X/d -0.15 while the energy resided in the vortex shedding
frequency component is low, this component is apparently dominant in the
spectrum. This is attributed to the reason that the wake resulted behind
the circular disk affects the flow pattern upstream.
It is concluded from this study that pressure fluctuations obtained on the
wall contain desirable information of vortex shedding frequency associated
with the wake resulting behind a confined circular disk. Vortex shedding
frequency can be extracted from wall pressure signal through a high-pass
filtering process or can be identified directly from frequency spectrum of
raw signal if the signal is obtained in the neighborhood of the maximum
pressure fluctuation being measured. This suggests a possibility to design
a vortex flowmeter with an axisymmetric bluff body while vortex shedding
frequency is obtained from wall pressure measurement.
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